IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 4241 Autonomous Spectrum Balancing for Digital Subscriber Lines Raphael Cendrillon, Member, IEEE, Jianwei Huang, Member, IEEE, Mung Chiang, Member, IEEE, and Marc Moonen, Fellow, IEEE Abstract—The main performance bottleneck of modern digital formance improvement in modern DSL systems remains to be subscriber line (DSL) networks is the crosstalk among different crosstalk, which is the interference generated among different lines (i.e., users). By deploying dynamic spectrum management lines in the same cable binder. The crosstalk is typically 10–20 (DSM) techniques and reducing excess crosstalk among users, a network operator can dramatically increase the data rates and ser- dB larger than the background noise, and direct crosstalk cance- vice reach of broadband access. However, current DSM algorithms lation (e.g., [1], [2]) is difficult in many cases, due to complexity suffer from either substantial suboptimality in typical deployment (both amount of computation needed and the requirements for scenarios or prohibitively high complexity due to centralized com- new chip sets) or unbundling requirement (i.e., incumbent ser- putation. This paper develops, analyzes, and simulates a new suite 1 of DSM algorithms for DSL interference-channel models called au- vice providers must rent certain lines to their competitors). tonomous spectrum balancing (ASB). The ASB algorithms utilize Recently, various dynamic spectrum management (DSM)2 al- the concept of a “reference line,” which mimics a typical victim line gorithms have been proposed to address this frequency-selec- in the interference channel. In ASB, each modem tries to minimize tive interference problem by dynamically optimizing transmis- the harm it causes to the reference line under the constraint of sion power spectra of different modems in DSL networks. DSM achieving its own target data-rate. Since the reference line is based on the statistics of the entire network, rather than any specific algorithms can significantly improve data rates over the cur- knowledge of the binder a modem operates in, ASB can be imple- rent practice of static spectrum management, which mandates mented autonomously without the need for a centralized spectrum spectrum mask or flat power backoff across all frequencies (i.e., management center. ASB has a low complexity and simulations tones). using a realistic simulator show that it achieves large performance gains over existing autonomous algorithms, coming close to the This paper develops, analyzes, and simulates a suite of DSM optimal rate region in some typical scenarios. Sufficient conditions algorithms for power allocation (or, equivalently, bit loading), for convergence of ASB are also proved. called autonomous spectrum balancing (ASB). Overcoming the Index Terms—Digital subscriber lines (DSLs), distributed al- bottlenecks in the state-of-the-art DSM algorithms, ASB is a set gorithm, dual decomposition, interference channel, multicarrier, of algorithms that, simultaneously, is autonomous (distributed power allocation, spectrum management. algorithm across the users without explicit real-time informa- tion exchange), has low complexity, is provably convergent under certain sufficient conditions, and achieves rate region I. INTRODUCTION close to the global optimum. The methods of “static pricing” A. Motivation and “frequency-selective waterfilling” developed in ASB may also be of interest to the general problems of decoupling cou- IGITAL SUBSCRIBER LINE (DSL) technologies trans- pled objective function and of multicarrier interference channel. Dform traditional voice-band copper channels into broad- band access systems, which are typically capable of delivering B. Related Work on DSM Algorithms data rates of several Mb/s per twisted-pair over a distance of 10 One of the first DSM algorithms is the Iterative Water-filling kft in the basic asymmetric DSL (ADSL). Despite over 160 mil- (IW) algorithm [3], where each line maximizes its own data rate lion DSL lines worldwide as of 2006, the major obstacle for per- by waterfilling over the noise and interference from other lines. The IW algorithm is autonomous, has a linear complexity in the Manuscript received September 1, 2006; revised November 30, 2006. The number of users and number of frequency tones, and has been associate editor coordinating the review of this manuscript and approving it for shown to converge in typical DSL deployments, e.g., [3], [4]. publication was Prof. Brian L. Evans. This work was supported in part by Al- catel-Bell and by the US NSF Grant CNS-0427677 and CCF-0448012. A por- Although IW can achieve near optimal performance in weak in- tion of this paper was has appeared in the IEEE Proceedings of the International terference channels, it is highly-suboptimal in the widely-en- Symposium of Information Theory, July 2006. countered near–far scenarios (which will be described in detail R. Cendrillon is with Marvell Hong Kong, Ltd., Mongkok, Hong Kong (e-mail: [email protected]; [email protected]). in Section II), such as mixed central office and remote terminal J. Huang and M. Chiang are with Department of Electrical Engi- neering, Princeton University, Princeton, NJ 08544 USA (e-mail: jianweih@ 1Although in an unbundled network DSM can be applied to in-domain lines, princeton.edu; [email protected]). in many cases out-of-domain lines cannot be coordinated, leading to some sub- M. Moonen is with the Department of Electrical Engineering, Katholieke optimality. Similarly the network management center can be used to coordinate Universiteit Leuven (K.U. Leuven,), ESAT/SISTA, B-3001 Leuven-Heverlee, lines in a centralized fashion, however such a network management center would Belgium (e-mail: [email protected]; [email protected]. require full knowledge of the network topology, which is often difficult to im- be). plement in practice. Further discussion can be found in Section I-B. Color versions of one or more of the figures in this paper are available online 2The DSM algorithms discussed in this paper are different from the “dynamic at http://ieeexplore.ieee.org. spectrum sharing” algorithms, which are used to refer to opportunistic sharing Digital Object Identifier 10.1109/TSP.2007.895989 of the spectrum resources in wireless communications. 1053-587X/$25.00 © 2007 IEEE 4242 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 TABLE I COMPARISON OF VARIOUS DSM ALGORITHMS deployments of ADSL and upstream VDSL. This is in part due While the band preference method calculates the bitloading in to the greedy and selfish nature of the algorithm. a distributed fashion, the band-preference coefficients (which Recently two optimal but centralized DSM algorithms were correspond to a spectral mask imposed on the waterfilling al- proposed, the Optimal Spectrum Balancing (OSB) algorithm gorithm) need to be calculated in some way, centralized or dis- [5] and the Iterative Spectrum Balancing (ISB) algorithm [6], tributed. This often requires the use of a centralized spectrum [7]. The OSB algorithm addresses the spectrum management management center. The performance of the band preference problem through the maximization of a weighted rate-sum method depends on the choice of the specific spectrum man- across all users, which explicitly takes into account the damage agement algorithm used. done to the other lines when optimizing each line’s spectra. IW, OSB, ISB, and SCALE mentioned above all assume syn- OSB has an exponential complexity in the number of users, chronous transmissions of the modems, which allows crosstalk making it intractable for DSL network with more than five to be modeled independently on each tone. This synchroniza- lines. As an improvement over the OSB algorithm, ISB was tion is rarely true in practice. Instead, the signal transmitted on proposed to implement the weighted-rate sum optimization in a particular tone of one modem will appear as crosstalk on a an iterative fashion over the users. This leads to a quadratic broad range of tones on the other modems. This inter-carrier- complexity in the number of users, which makes the ISB interference (ICI) complicates the DSM problem further. The feasible for networks with a relatively large number of users. state-of-the-art results for asynchronous transmissions are the However, an even more critical issue is that both OSB and two centralized greedy algorithms proposed in [10], bit-sub- ISB are centralized algorithms, which rely on a centralized net- tracting and bit-adding algorithms. Both algorithms start from work management center (NMC) to optimize the power spectral the power spectral density (PSD) obtained with the ISB algo- density (PSD) for all modems. The NMC requires knowledge rithm in the synchronous case, and search for local optimal solu- of the crosstalk channels among all lines and all background tions in the neighborhood by taking ICI into account. But again noise. Identification and transmission of crosstalk channel mea- these are centralized algorithms. surements back to the NMC are not supported in existing stan- dards either. The operation of NMC requires a lot of overhead, C. Summary of Contributions in terms of both bandwidth and infrastructure. Furthermore, reg- The advantages of ASB algorithms are summarized as fol- ulatory requirements on unbundling service make it impossible lows. First of all, ASB is autonomous: it can be applied in a to perform a centralized optimization. Finally, many lines in the distributed fashion across users with no explicitly information same binder terminate on different quad cards in the DSL Ac- exchange in real-time. Furthermore, the algorithm has low com- cess Multiplexer because customers in the same neighborhood plexity in both the number of users and tones, and is proved to sign up for service at different times, which makes it hard to be convergent under certain sufficient conditions on the channel have central coordination even if one can tolerate the costs. gains. In the synchronous case, the ASB algorithm has a sim- A semi-centralized DSM algorithm called SCALE is pro- ilar complexity as IW, but in the near–far scenario achieves a posed in [8].